一类非线性发展方程孤立波求解的广义Padé逼近法  

Solitary Wave Solutions of Certain Nonlinear Evolution Equations via Generalized Padé Approximation Method

作　　者：李震波 LI Zhen-bo(School of Mathematics and Physics,University of South China,Hengyang 421001,China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《数学的实践与认识》2022年第12期180-191,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11747147);湖南省自然科学基金(2019JJ50515);湖南省教育厅科学研究项目(21B0419)。

摘　　要：将广义Padé逼近方法推广至非线性发展方程孤立波的求解,并利用该方法研究了描述磁化等离子体演化过程的改进的Zakharov-Kuznetsov方程、描述弹性杆的纵向形变波传播的广义Pochhammer-Chree方程以及在非线性光学研究中有着重要作用的广义Drinfeld-Sokolov方程,求得了上述方程的高精度孤立波解.结果表明,广义Padé逼近方法在非线性发展方程孤波解的求解中依然有效,既推广了广义Padé逼近方法的适用范围,也为非线性发展方程孤立波的求解提供了新的思路和参考方法.In this paper,the generalized Padé approximation method is extended to Solve solitary waves of nonlinear evolution equations.Using this method,the improved Zakharov Kuznetsov equation describing the evolution of magnetized plasma,the generalized Pochhammer chree equation describing the longitudinal deformation wave propagation of elastic rod and the generalized Drinfeld Sokolov equation which plays an important role in the study of nonlinear optics are studied.High-precision solitary wave solutions of the above equations are obtained.The results show that the generalized Padé approximation method is still effective in solving solitary wave solutions of nonlinear evolution equation.It means that the application scope of the generalized Padé approximation method is extended,and a new idea and reference method for solving solitary waves of nonlinear evolution equations are provided.

关 键 词：非线性发展方程 孤立波解 广义Padé逼近 

分 类 号：O175.29[理学—数学]